%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU660^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n008.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Fri Oct 3 08:02:09 PM UTC 2025 % Result : Theorem 4.01s 4.23s % Output : Proof 4.10s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SEU660^2 : TPTP v9.2.0. Released v3.7.0. % 0.12/0.14 % Command : duper %s % 0.13/0.34 % Computer : n008.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Oct 3 05:21:53 EDT 2025 % 0.13/0.34 % CPUTime : % 4.01/4.23 SZS status Theorem for theBenchmark.p % 4.01/4.23 SZS output start Proof for theBenchmark.p % 4.01/4.23 Clause #0 (by assumption #[]): Eq % 4.01/4.23 (Eq cartprodmempair1 % 4.01/4.23 (∀ (A B Xu : Iota), % 4.01/4.23 in Xu (cartprod A B) → Exists fun Xx => And (in Xx A) (Exists fun Xy => And (in Xy B) (Eq Xu (kpair Xx Xy))))) % 4.01/4.23 True % 4.01/4.23 Clause #1 (by assumption #[]): Eq (Eq setukpairinjR (∀ (Xx Xy Xz Xu : Iota), Eq (kpair Xx Xy) (kpair Xz Xu) → Eq Xy Xu)) True % 4.01/4.23 Clause #2 (by assumption #[]): Eq (Not (cartprodmempair1 → setukpairinjR → ∀ (A B Xx Xy : Iota), in (kpair Xx Xy) (cartprod A B) → in Xy B)) True % 4.01/4.23 Clause #3 (by clausification #[2]): Eq (cartprodmempair1 → setukpairinjR → ∀ (A B Xx Xy : Iota), in (kpair Xx Xy) (cartprod A B) → in Xy B) False % 4.01/4.23 Clause #4 (by clausification #[3]): Eq cartprodmempair1 True % 4.01/4.23 Clause #5 (by clausification #[3]): Eq (setukpairinjR → ∀ (A B Xx Xy : Iota), in (kpair Xx Xy) (cartprod A B) → in Xy B) False % 4.01/4.23 Clause #6 (by clausification #[5]): Eq setukpairinjR True % 4.01/4.23 Clause #7 (by clausification #[5]): Eq (∀ (A B Xx Xy : Iota), in (kpair Xx Xy) (cartprod A B) → in Xy B) False % 4.01/4.23 Clause #8 (by clausification #[7]): ∀ (a : Iota), Eq (Not (∀ (B Xx Xy : Iota), in (kpair Xx Xy) (cartprod (skS.0 0 a) B) → in Xy B)) True % 4.01/4.23 Clause #9 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (B Xx Xy : Iota), in (kpair Xx Xy) (cartprod (skS.0 0 a) B) → in Xy B) False % 4.01/4.23 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), % 4.01/4.23 Eq (Not (∀ (Xx Xy : Iota), in (kpair Xx Xy) (cartprod (skS.0 0 a) (skS.0 1 a a_1)) → in Xy (skS.0 1 a a_1))) True % 4.01/4.23 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), % 4.01/4.23 Eq (∀ (Xx Xy : Iota), in (kpair Xx Xy) (cartprod (skS.0 0 a) (skS.0 1 a a_1)) → in Xy (skS.0 1 a a_1)) False % 4.01/4.23 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), % 4.01/4.23 Eq % 4.01/4.23 (Not % 4.01/4.23 (∀ (Xy : Iota), in (kpair (skS.0 2 a a_1 a_2) Xy) (cartprod (skS.0 0 a) (skS.0 1 a a_1)) → in Xy (skS.0 1 a a_1))) % 4.01/4.23 True % 4.01/4.23 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), % 4.01/4.23 Eq (∀ (Xy : Iota), in (kpair (skS.0 2 a a_1 a_2) Xy) (cartprod (skS.0 0 a) (skS.0 1 a a_1)) → in Xy (skS.0 1 a a_1)) % 4.01/4.23 False % 4.01/4.23 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 a_3 : Iota), % 4.01/4.23 Eq % 4.01/4.23 (Not % 4.01/4.23 (in (kpair (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) (cartprod (skS.0 0 a) (skS.0 1 a a_1)) → % 4.01/4.23 in (skS.0 3 a a_1 a_2 a_3) (skS.0 1 a a_1))) % 4.01/4.23 True % 4.01/4.23 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 a_3 : Iota), % 4.01/4.23 Eq % 4.01/4.23 (in (kpair (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) (cartprod (skS.0 0 a) (skS.0 1 a a_1)) → % 4.01/4.23 in (skS.0 3 a a_1 a_2 a_3) (skS.0 1 a a_1)) % 4.01/4.23 False % 4.01/4.23 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 a_3 : Iota), % 4.01/4.23 Eq (in (kpair (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) (cartprod (skS.0 0 a) (skS.0 1 a a_1))) True % 4.01/4.23 Clause #17 (by clausification #[15]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 3 a a_1 a_2 a_3) (skS.0 1 a a_1)) False % 4.01/4.23 Clause #18 (by clausification #[1]): Eq setukpairinjR (∀ (Xx Xy Xz Xu : Iota), Eq (kpair Xx Xy) (kpair Xz Xu) → Eq Xy Xu) % 4.01/4.23 Clause #19 (by forward demodulation #[18, 6]): Eq True (∀ (Xx Xy Xz Xu : Iota), Eq (kpair Xx Xy) (kpair Xz Xu) → Eq Xy Xu) % 4.01/4.23 Clause #20 (by clausification #[19]): ∀ (a : Iota), Eq (∀ (Xy Xz Xu : Iota), Eq (kpair a Xy) (kpair Xz Xu) → Eq Xy Xu) True % 4.01/4.23 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (∀ (Xz Xu : Iota), Eq (kpair a a_1) (kpair Xz Xu) → Eq a_1 Xu) True % 4.01/4.23 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), Eq (∀ (Xu : Iota), Eq (kpair a a_1) (kpair a_2 Xu) → Eq a_1 Xu) True % 4.01/4.23 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 a_3 : Iota), Eq (Eq (kpair a a_1) (kpair a_2 a_3) → Eq a_1 a_3) True % 4.01/4.23 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (Eq (kpair a a_1) (kpair a_2 a_3)) False) (Eq (Eq a_1 a_3) True) % 4.01/4.23 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (Eq a a_1) True) (Ne (kpair a_2 a) (kpair a_3 a_1)) % 4.01/4.23 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne (kpair a a_1) (kpair a_2 a_3)) (Eq a_1 a_3) % 4.01/4.23 Clause #28 (by clausification #[0]): Eq cartprodmempair1 % 4.10/4.26 (∀ (A B Xu : Iota), % 4.10/4.26 in Xu (cartprod A B) → Exists fun Xx => And (in Xx A) (Exists fun Xy => And (in Xy B) (Eq Xu (kpair Xx Xy)))) % 4.10/4.26 Clause #29 (by forward demodulation #[28, 4]): Eq True % 4.10/4.26 (∀ (A B Xu : Iota), % 4.10/4.26 in Xu (cartprod A B) → Exists fun Xx => And (in Xx A) (Exists fun Xy => And (in Xy B) (Eq Xu (kpair Xx Xy)))) % 4.10/4.26 Clause #30 (by clausification #[29]): ∀ (a : Iota), % 4.10/4.26 Eq % 4.10/4.26 (∀ (B Xu : Iota), % 4.10/4.26 in Xu (cartprod a B) → Exists fun Xx => And (in Xx a) (Exists fun Xy => And (in Xy B) (Eq Xu (kpair Xx Xy)))) % 4.10/4.26 True % 4.10/4.26 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), % 4.10/4.26 Eq % 4.10/4.26 (∀ (Xu : Iota), % 4.10/4.26 in Xu (cartprod a a_1) → Exists fun Xx => And (in Xx a) (Exists fun Xy => And (in Xy a_1) (Eq Xu (kpair Xx Xy)))) % 4.10/4.26 True % 4.10/4.26 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), % 4.10/4.26 Eq % 4.10/4.26 (in a (cartprod a_1 a_2) → Exists fun Xx => And (in Xx a_1) (Exists fun Xy => And (in Xy a_2) (Eq a (kpair Xx Xy)))) % 4.10/4.26 True % 4.10/4.26 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), % 4.10/4.26 Or (Eq (in a (cartprod a_1 a_2)) False) % 4.10/4.26 (Eq (Exists fun Xx => And (in Xx a_1) (Exists fun Xy => And (in Xy a_2) (Eq a (kpair Xx Xy)))) True) % 4.10/4.26 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 a_3 : Iota), % 4.10/4.26 Or (Eq (in a (cartprod a_1 a_2)) False) % 4.10/4.26 (Eq % 4.10/4.26 (And (in (skS.0 4 a_1 a_2 a a_3) a_1) % 4.10/4.26 (Exists fun Xy => And (in Xy a_2) (Eq a (kpair (skS.0 4 a_1 a_2 a a_3) Xy)))) % 4.10/4.26 True) % 4.10/4.26 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 a_3 : Iota), % 4.10/4.26 Or (Eq (in a (cartprod a_1 a_2)) False) % 4.10/4.26 (Eq (Exists fun Xy => And (in Xy a_2) (Eq a (kpair (skS.0 4 a_1 a_2 a a_3) Xy))) True) % 4.10/4.26 Clause #37 (by clausification #[35]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.10/4.26 Or (Eq (in a (cartprod a_1 a_2)) False) % 4.10/4.26 (Eq (And (in (skS.0 5 a_2 a a_1 a_3 a_4) a_2) (Eq a (kpair (skS.0 4 a_1 a_2 a a_3) (skS.0 5 a_2 a a_1 a_3 a_4)))) % 4.10/4.26 True) % 4.10/4.26 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.10/4.26 Or (Eq (in a (cartprod a_1 a_2)) False) (Eq (Eq a (kpair (skS.0 4 a_1 a_2 a a_3) (skS.0 5 a_2 a a_1 a_3 a_4))) True) % 4.10/4.26 Clause #39 (by clausification #[37]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Or (Eq (in a (cartprod a_1 a_2)) False) (Eq (in (skS.0 5 a_2 a a_1 a_3 a_4) a_2) True) % 4.10/4.26 Clause #40 (by clausification #[38]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.10/4.26 Or (Eq (in a (cartprod a_1 a_2)) False) (Eq a (kpair (skS.0 4 a_1 a_2 a a_3) (skS.0 5 a_2 a a_1 a_3 a_4))) % 4.10/4.26 Clause #41 (by superposition #[40, 16]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.10/4.26 Or % 4.10/4.26 (Eq (kpair (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) % 4.10/4.26 (kpair (skS.0 4 (skS.0 0 a) (skS.0 1 a a_1) (kpair (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) a_4) % 4.10/4.26 (skS.0 5 (skS.0 1 a a_1) (kpair (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) (skS.0 0 a) a_4 a_5))) % 4.10/4.26 (Eq False True) % 4.10/4.26 Clause #43 (by superposition #[39, 16]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.10/4.26 Or % 4.10/4.26 (Eq % 4.10/4.26 (in (skS.0 5 (skS.0 1 a a_1) (kpair (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) (skS.0 0 a) a_4 a_5) % 4.10/4.26 (skS.0 1 a a_1)) % 4.10/4.26 True) % 4.10/4.26 (Eq False True) % 4.10/4.26 Clause #45 (by clausification #[43]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.10/4.26 Eq % 4.10/4.26 (in (skS.0 5 (skS.0 1 a a_1) (kpair (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) (skS.0 0 a) a_4 a_5) % 4.10/4.26 (skS.0 1 a a_1)) % 4.10/4.26 True % 4.10/4.26 Clause #46 (by clausification #[41]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.10/4.26 Eq (kpair (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) % 4.10/4.26 (kpair (skS.0 4 (skS.0 0 a) (skS.0 1 a a_1) (kpair (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) a_4) % 4.10/4.26 (skS.0 5 (skS.0 1 a a_1) (kpair (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) (skS.0 0 a) a_4 a_5)) % 4.10/4.26 Clause #48 (by superposition #[46, 26]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 4.10/4.26 Or (Ne (kpair a a_1) (kpair (skS.0 2 a_2 a_3 a_4) (skS.0 3 a_2 a_3 a_4 a_5))) % 4.10/4.26 (Eq a_1 (skS.0 5 (skS.0 1 a_2 a_3) (kpair (skS.0 2 a_2 a_3 a_4) (skS.0 3 a_2 a_3 a_4 a_5)) (skS.0 0 a_2) a_6 a_7)) % 4.10/4.26 Clause #49 (by equality resolution #[48]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.10/4.26 Eq (skS.0 3 a a_1 a_2 a_3) % 4.10/4.26 (skS.0 5 (skS.0 1 a a_1) (kpair (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) (skS.0 0 a) a_4 a_5) % 4.10/4.26 Clause #51 (by backward demodulation #[49, 45]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 3 a a_1 a_2 a_3) (skS.0 1 a a_1)) True % 4.10/4.26 Clause #54 (by superposition #[51, 17]): Eq True False % 4.10/4.26 Clause #55 (by clausification #[54]): False % 4.10/4.26 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------